For his Ph.D. in astrophysics, Chris Farrell spent five years mining data from a giant particle accelerator. Now, he spends his days analyzing ratings for Yelp Inc.'s online business-review site.

Mr. Farrell, 28 years old, is a data scientist, a job title that barely existed three years ago but since has become one of the hottest corners of the high-tech labor market. Retailers, banks, heavy-equipment makers and matchmakers all want...